关于Riccati微分方程的四元数推广
On a quaternionic generalisation of the Riccati differential equation
摘要：
证明了四元数偏微分方程是Riccati常微分方程的推广，并建立了它与薛定谔方程的关系。各种方法来寻找特殊的解决方案的问题进行了探讨，并给出了两个定理的推广欧拉Riccati微分方程，这对应于四元数方程。
英文摘要：
A quaternionic partial differential equation is shown to be a generalisation of the Riccati ordinary differential equation and its relationship with the Schrodinger equation is established. Various approaches to the problem of finding particular solutions are explored, and the generalisations of two theorems of Euler on the Riccati differential equation, which correspond to the quaternionic equation, are given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
